Multiply the following complex numbers: $({-2-3i}) \cdot ({-2})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2-3i}) \cdot ({-2}) = $ $ ({-2} \cdot {-2}) + ({-2} \cdot {0}i) + ({-3}i \cdot {-2}) + ({-3}i \cdot {0}i) $ Then simplify the terms: $ (4) + (0i) + (6i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (0 + 6)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (0 + 6)i - 0 $ The result is simplified: $ (4 - 0) + (6i) = 4+6i $